Heterogeneous Diffusion in a Reversible Gel
Pablo I. Hirtado Fernandez
Université de Grenade, Espagne
Mon, Nov. 27th 2006, 14:15
Salle Claude Itzykson, Bât. 774, Orme des Merisiers
Many soft materials can be described as network-forming liquids, i.e., as
dispersions of particles connected by transient elastic bridges. Their
cooperative dynamic behavior exhibits striking features, characterized by
non-linearities (shear thinning and thickening), instabilities (shear
banding, rheochaos) and heterogeneities, which lack any microscopic
understanding. I will introduce in this talk a simplified model of
transient-network liquid, composed by particles and bridging polymers,
amenable to detailed theoretical, numerical and experimental analysis.
Three different phases - sol, gel and coexistence - conform the model
phase diagram. The gel phase is stable and broad, allowing a good
microscopic characterization of gelation and gel dynamics. As we cross the
sol-gel percolation line, a time-scale separation emerges, with a
microscopic time scale $t_1$, associated with local particle rearrangements,
and a mesoscopic one, $t_2$, controled by the polymer residence time. For
times shorter than $t_2$ the transient-network liquid behave as a disordered
solid. The dynamics in the gel phase is highly heterogeneous, and
resembles that observed in glassy systems and other disordered materials.
In particular, the van Hove distribution for particle displacements is
strongly non-gaussian, with a bimodal structure due to the coexistence of
arrested and mobile particles in the gel. The simplicity of the model
allows us to propose a simple mathematical description that captures the
observed dynamic heterogeneities, also providing more general insights
into the origin of dynamic heterogeneity in disordered materials.